A power CCDF curve is frequently used in RF applications to provide critical information about the signals encountered in RF systems, for example in modern 3rd Generation (3G) digitally modulated radio systems. The power CCDF curve consists of a curve relating the percentage of time a radio signal spends at or above a particular power level. It is usually shown as a graph of the ratio of the instantaneous power to the average power against percentage of time that the signal power is at, or above, the power specified in the X axis. Both axes of the graph are usually logarithmic.
Perhaps the most important application of power CCDF curves is to specify completely the power characteristics of the signals that will be mixed, amplified and decoded in communication systems. For example, 3G systems combine multiple channels resulting in a peak-to-average power ratio that is dependent upon not only the number of channels, but also which specific channels are used. This signal characteristic can lead to higher distortion unless the peak power levels are accounted for in the design of system components, such as amplifiers and mixers.
As well as examining a graph, a user may also request the power level at which a certain percentage of the measurements lie in excess. Typical percentages lie in the range of 0.01% to 0.0001%. For example, if a sample of 100,000 measurements has taken place and if the user requires the power ratio at which 0.01% of samples lie in excess then there will be 10 samples lying above the 0.01% percentage point (0.01%= 1/10,000). Normally the ratio of the tenth largest sample to the calculated average power is returned.
Such a CCDF curve appears in several kinds of measurement instrument from power meters to spectrum analysers and a few others as well. All these instruments have needed to generate a histogram of the power values received and then convert it to the CCDF graph. This task is carried out by sampling the incoming signal using an Analogue-to-Digital converter (ADC), storing the resulting captured samples in memory and then calculating a histogram of the received values by scanning the captured samples, converting each received value from voltage to power if necessary, and then summing each value or small set of values into many accumulators before using the resultant table of occurrences to draw a graph and/or work out the percentages.
A typical system can take around 5 seconds to measure and process 100,000 samples. In most known systems, samples tend to be captured at high speed for a short time, then the captured samples are processed and then another batch of samples are taken. Current ADC technologies are capable of running at speeds in the range of 10M samples/second up to, in some cases, several Giga samples per second. What this means is that a typical system will take very short snapshots of a waveform, which can result in missing the elusive high peak levels that have the greatest effect on the resulting measurement numbers.
It can also be readily seen that 100,000 samples provides only ten samples “above the line” for a 0.01% measurement. Measurements of 0.001% or 0.0001% would require orders of magnitude more time to get the same accuracy. Furthermore, ten samples is, in some circumstances, not a sufficiently large number on which to base an accurate measurement.